Chapter 10, Problem 10.93E

Interpretation Introduction

Interpretation:

The expression for the average value of position for ${\Psi }_{10}$ for a particle-in-a-box is to be integrated numerically. The answer for the same is to be explained.

Concept introduction:

The Schrödinger equation is used to find the allowed energy levels for electronic transitions in the quantum mechanics. It is generally expressed as follows.

$\stackrel{⌢}{\mathrm{H}}\Psi =\text{E}\Psi$

Where,

• $\stackrel{⌢}{\text{H}}$ is the Hamiltonian operator.

• $\Psi$ is the wavefunction.

• $\text{E}$ is the energy.

The energy obtained after applying the operator on wavefunction is known as the eigen value for the wavefunction.